A conducting loop in the shape of a right angled isosceles triangle of height 10 cm is kept such that the $90^{0}$ vertex is very close to an infinitely long conducting wire (see the figure) . The wire is electrically insulated from the loop and the hypotenuse of the triangle is parallel to the wire . The current in the triangular loop is in counterclockwise direction and increased at a constant rate of ${10As}^{-1}$ . Which of the following statement (s) (are) true?

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^{There is a repulsive force between the wire and the loop}

The induced current in the wire is in opposite direction to the current along the hypotenuse

If the loop is rotated at a constant angular speed about the wire, an additional emf $(\frac{μ_{0}}{π})$ volt is induced in the wire

The magnitude of induced $emf$ in the wire is $(\frac{μ_{0}}{π})$ Volt

answer is A, D.

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Detailed Solution

The flux passing through the triangular wire if I current flows through the infinitely long conducting wire $= \int_{0}^{0.1} \frac{μ_{0} i}{2 π x} \times 2 x d x$

$ϕ = \frac{μ_{0} i}{10 π} = M i$

$\frac{dl}{dt} {=10 AS}^{-1}$

$∴ M = \frac{μ_{0}}{10 π}$ Induced emf in the wire

$= M \frac{d i}{d t} = \frac{μ_{0}}{10 π} \times 10 = \frac{μ_{0}}{π}$

As the current in the triangular wire is decreasing the induced current in AB is in the same direction as the current in the hypotenuse of the triangular wire . Therefore force will be repulsive

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